I'm reading a book where the autocorrelation of white noise is expressed as:
What is the term $Q(k)$ and why is is expressed as an average value of a dot product ?
I’m guessing your book is on Kalman filters and $u(k)$ is a term in a state variable equation of a linear system. If so, it is a vector and the components of that vector at some time index $k$ can be correlated with each other but are independent with respect to $k$.
it isn’t a dot product, it is an outer product.